Physics-Aware Multifidelity Bayesian Optimization: a Generalized Formulation

The adoption of high-fidelity models for many-query optimization problems is majorly limited by the significant computational cost required for their evaluation at every query. Multifidelity Bayesian methods (MFBO) allow to include costly high-fidelity responses for a sub-selection of queries only, and use fast lower-fidelity models to accelerate the optimization process. State-of-the-art methods rely on a purely data-driven search and do not include explicit information about the physical context. This paper acknowledges that prior knowledge about the physical domains of engineering problems can be leveraged to accelerate these data-driven searches, and proposes a generalized formulation for MFBO to embed a form of domain awareness during the optimization procedure. In particular, we formalize a bias as a multifidelity acquisition function that captures the physical structure of the domain. This permits to partially alleviate the data-driven search from learning the domain properties on-the-fly, and sensitively enhances the management of multiple sources of information. The method allows to efficiently include high-fidelity simulations to guide the optimization search while containing the overall computational expense. Our physics-aware multifidelity Bayesian optimization is presented and illustrated for two classes of optimization problems frequently met in science and engineering, namely design optimization and health monitoring problems.

Active Learning and Bayesian Optimization: a Unified Perspective to Learn with a Goal

Both Bayesian optimization and active learning realize an adaptive sampling scheme to achieve a specific learning goal. However, while the two fields have seen an exponential growth in popularity in the past decade, their dualism has received relatively little attention. In this paper, we argue for an original unified perspective of Bayesian optimization and active learning based on the synergy between the principles driving the sampling policies. This symbiotic relationship is demonstrated through the substantial analogy between the infill criteria of Bayesian optimization and the learning criteria in active learning, and is formalized for the case of single information source and when multiple sources at different levels of fidelity are available. We further investigate the capabilities of each infill criteria both individually and in combination on a variety of analytical benchmark problems, to highlight benefits and limitations over mathematical properties that characterize real-world applications.

Non-Myopic Multifidelity Bayesian Optimization

Bayesian optimization is a popular framework for the optimization of black box functions. Multifidelity methods allows to accelerate Bayesian optimization by exploiting low-fidelity representations of expensive objective functions. Popular multifidelity Bayesian strategies rely on sampling policies that account for the immediate reward obtained evaluating the objective function at a specific input, precluding greater informative gains that might be obtained looking ahead more steps. This paper proposes a non-myopic multifidelity Bayesian framework to grasp the long-term reward from future steps of the optimization. Our computational strategy comes with a two-step lookahead multifidelity acquisition function that maximizes the cumulative reward obtained measuring the improvement in the solution over two steps ahead. We demonstrate that the proposed algorithm outperforms a standard multifidelity Bayesian framework on popular benchmark optimization problems.